Future wireless local area networks (WLANs) will use orthogonal frequency division multiplexing (OFDM) as the modulation method. OFDM is well suited to the requirements of localised, broadband communications and has been shown to operate at raw data rates of up to 54 Mbit/s in demonstration conditions.
To provide error free communication it is necessary for any communications receiver to estimate channel and system induced distortions. A number of methods of estimating these parameters in OFDM systems have previously been proposed (see for example L. J. Cimini, Y Li, “Orthogonal frequency division multiplexing for wireless channels”, Tutorial Presentation, Proc IEEE Globecom '98, November 1998 and T. Keller, L. Hanzo, “Adaptive multicarrier modulation: a convenient framework for time-frequency processing in wireless communications”, Proc IEEE, vol 88, no 5, May 2000, pp 611-640). Methods have been proposed based on pilot symbols and based on null symbols (see for example P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction”, IEEE Trans. Commun., vol 42, October 1994, pp 2908-2914, J. Aldis, M. P. Altrhoff, R. van Nee “Physical layer architecture and performance in the WAND user trial system”, Proc. ACTS Mobile Summit '96, November 1996, pp 196-203, G. Santella, “A frequency and symbol synchronization system for OFDM signals: architecture and simulation results”, IEEE Trans. Vehic. Technol., vol 49, no 1, January 2000, pp 254-275). Assuming that initial synchronisation has been achieved, methods to track these parameters from OFDM data have also been proposed (see for example H. Steendam, M. Moeneclaey, “Analysis and optimisation of the performance of OFDM on frequency-selective time-selective fading channels”, IEEE Trans. Commun., vol 47, no 12, December 1999, pp 1811-1819). Alternative tracking and/or adaptive channel estimation methods have been proposed which are based on embedded pilot tones (see for example Y. Li, L. J. Cimini Jr., N. R. Sollenberger, “Robust channel estimation for OFDM systems with rapid dispersive fading channels”, IEEE Trans. Commun., vol 46, April 1998, pp 902-915).
In a communications system the wide-sense stationary uncorrelated scatterers (WSS-US) model of the low pass-equivalent multipath fading channel may be represented by the time-varying impulse response
                              c          ⁡                      (                          τ              ;              t                        )                          =                              ∑                          m              =              1                                      M              ⁡                              (                t                )                                              ⁢                                                    a                m                            ⁡                              (                t                )                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                                  ⁢                                                      ϕ                    m                                    ⁡                                      (                    t                    )                                                                        ⁢                          δ              ⁡                              [                                  τ                  -                                                            τ                      m                                        ⁡                                          (                      t                      )                                                                      ]                                                                1      which is a function of time-delay τ and time t; where am(t) is the amplitude, φm(t)=2πƒCτm(t) is the phase of carrier frequency ƒC, and τm(t) is the time-delay of the mth of M bins or echoes measured at time t. For a narrowband signal, that is one for which the signal bandwidth B is less than the channel coherence bandwidth (Δƒ)C, the “flat” fading multipath channel reduces to
                                                                        c                ⁡                                  (                  t                  )                                            ⁢                              =                .                            ⁢                            ⁢                              c                ⁡                                  (                                      0                    ;                    t                                    )                                                                                                        =                            ⁢                                                a                  ⁡                                      (                    t                    )                                                  ⁢                                  ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                                          ϕ                      ⁡                                              (                        t                        )                                                                                            ⁢                                  δ                  ⁡                                      [                                          τ                      -                                                                        τ                          0                                                ⁡                                                  (                          t                          )                                                                                      ]                                                                                                  2      where a(t) is the amplitude, φ(t) is the phase and τ0(t) is the excess delay imposed by the multiplicative channel. Note that all the above quantities are time-varying. In a WLAN the channel may be narrowband or may be a frequency-selective multipath fading channel. In frequency-selective multipath channels the simplification of equation (2) does not apply.
In addition to the channel-induced distortions, frequency differences in the transmitter and receiver RF local oscillators and sample clocks due to component tolerances introduce, respectively, frequency and timing errors. Thus, for a narrowband channel, the received sampled signal may be expressed as
                                          r            δ                    ⁡                      (            nT            )                          =                              ∑                          n              =              0                                      N              -              1                                ⁢                                    s              ⁡                              (                t                )                                      ⁢                          a              ⁡                              (                t                )                                      ⁢                          ⅇ                              -                                  j                  ⁡                                      [                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  v                          ⁡                                                      (                            t                            )                                                                          ⁢                        t                                            +                                              θ                        ⁡                                                  (                          t                          )                                                                                      ]                                                                        ⁢                          δ              ⁡                              [                                  t                  -                  nT                  -                                                            τ                      s                                        ⁡                                          (                      t                      )                                                                      ]                                                                3      where ν(t) is the frequency-, θ(t) is the phase- and τS(t) is the time-offset induced by the combination of channel and system distortions, n is the index of N samples of received signal s(t) at sample period T and the superscript δ denotes a sampled signal. The time-varying frequency offset ν(t) is a composite of Doppler shift and RF local oscillator offset, the time-varying phase offset θ(t) is the instantaneous snapshot of these composite frequency errors expressed as a time-varying phase difference between the transmitted and received baseband signals, the time-varying time-offset τS(t) is a composite of the excess delay and sample clock phase offset, and n=0 represents the start-of-packet sample. Each of these parameters requires estimation by the receiver and, since all but n are time-varying quantities, each estimate must be updated through the reception process. These distortions occur for all narrowband channels regardless fo the modulation scheme used to transmit data through the channel.
A number of methods for estimating these parameters in ODFM systems have been proposed. The proposed methods include methods based on pilot symbols and methods based on null symbols. Assuming that initial synchronisation has been achieved methods for tracking the parameters have also been proposed.